A methodology for modeling the interaction between turbulence and non-linearity of the equation of state

• Published in: Physics of fluids (1994) 2022-01, Vol.34 (1)
• Main Authors: Poormahmood, A., Salehi, M. Mahdi, Farshchi, M.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Critical pressure; Equations of state; Fluid dynamics; Fluid flow; Gas flow; Ideal gas; Jet flow; Mach number; Methodology; Mixing layers (fluids); Probability density functions; Real gases; Temperature ratio; Turbulence; Turbulent flow; Turbulent jets; Turbulent mixing; Working fluids
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0076099

Computational fluid dynamics simulation of turbulent mixing layers with significant density variations may require a closure model for the interaction between the unresolved turbulence scales and the equation of state (EoS). Ideal gas flows with significant temperature variations and real gas flows near the critical pressure and temperature undergo non-linear density variations. Therefore, using the first moment closure to obtain the mean/filtered density field from the EoS in a pressure-based computational fluid dynamics approach may result in significant modeling errors. In this work, a methodology is formulated to determine whether or not a closure model is required in the context of low-Mach number mixing layers. The methodology is based on a presumed probability density function closure modeling approach to develop a regime diagram in terms of four non-dimensional variables: reduced pressure, normalized lower temperature, temperature ratio across the mixing layer, and normalized variance of temperature fluctuations. The regime diagram clearly outlines conditions requiring no closure model and is approximately universal for different working fluids in a mixing layer. A posteriori simulations of a turbulent jet flow at different thermodynamic conditions show that the regime diagram effectively determines the necessity of closure modeling for density.